Copyright law governs the distribution of copyrighted works, not use. In most EULAs in proprietary software there are lots of clauses how you can use the software and how you can't, but such clauses do not belong under the copyright law and are invalid in most countries.

A EULA is an "End User License and Agreement".

The license part is the part that grants permissions for the activities covered by copyright law, which as you say, essentially deals only with distribution.

The agreement part is purported to be an additional contract between the software vendor and the user, which is supposed to cover all kinds of restrictions for acts which are not covered by copyrighjt law at all. A contract is supposed to be agreed to by all parties. EULAs are claimed to be contractually binding, having purportedly gained mutual agreement when a user clicks "I Agree".

Contract agreements are held to be valid in all countries, AFAIK.

IMO, it is a wise idea to never click on "I Agree" for a EULA if you can possibly avoid it. You are agreeing to be bound by all sorts of conditions and restraints that no law requires you to be bound to.

In contrast, the GPL is a license only. It gives conditional permissions for the activities covered by copyright law. In addition, it gives unconditional permissions for other activities related to the software (such as "using" it, i.e. running it) which are not covered under copyright law.

I am not clear why the unconditional permissions, for those acts not covered by copyright law, are required. After all, it is not illegal to read a book which you have not purchased (e.g. you can borrow an book from a friend) ... if it were illegal to read we would have no libraries. So why should it be illegal to run software?

Anyway, the GPL gives you the permissions, required or not, just in case there is any doubt.

The GPL is not an agreement, it is merely a document granting permissions. It is a license only.